The other option is, of course, that I'm insanely neurotic and need to stop thinking about this?

What I've come up with so far is that "D." is the best solutionif you have yet to say "Hi" to that person today. Otherwise, if you've already greeted them, then "A." is the best solution. This seems to go over the most favorably with the co-workers, so I assume they've all gone over this scenario themselves.